Cosmic Baton Girl Comet-san

Comet is the young princess of the star kingdom Harmonica, but on the evening of an importent party the prince of another star kingdom vanishes - Comet follows him to earth to find and bring back the prince, which is not as easy as she thinks.

This is an all animated remake of the old Comet-san series from the sixties (it was mainly live action but used some cel animation for special effects and some of the characters).